Paul Glimcher is a neuroscientist and behavioral psychologist who founded the new field of neuroeconomics.

Glimcher has been unusual among scientists to take seriously the significance of quantum indeterminacy in the biological sciences. Since Galileo, Kepler, and Newton, the paradigm of quantitative and mathematical science has been predictability. This in turn depends above all on causal laws, which appeared to most thinkers to require determinism. Reductionists argue that biology is reducible to physics and chemistry and thus subject to the same causal laws.

We now know that determinism is an emergent phenomenon, not yet present when the universe consisted of only radiation and a few elementary particles for the first few hundred thousand years.

Macroscopic bodies like the planets are aggregates of vast numbers of particles that average over the microscopic quantum uncertainty. Their behavior is the statistical consequence of the law of large numbers. It was macroscopic bodies, especially planets, but also billiard balls, that gave us Newton's laws, driving our intuition that everything must follow such "universal" laws.

Glimcher makes the case that human and animal behavior, dependent ultimately on very small brain structures that approach the quantum level, may involve the irreducible indeterminacy of quantum mechanics and challenge the standard assumptions of behavioral science.

Since René Descartes, the bodies of humans and animals have been assumed to be machines following deterministic and causal laws. Descartes drew diagrams of the reflex arc of afferent signals from a foot feeling pain, up to the brain, and efferent signals back down to pull the muscles away. (Descartes located freedom of the will in the separate substance of a human mind. Animals lacked such freedom.)

This reflex arc of causes and effects, and the related metaphor of biological processes as "mechanisms," prominent in the great twentieth century work of Charles Sherrington, is still the most common textbook explanation today.

Glimcher is surprised to find that the great Erwin Schrödinger, one of the founders of quantum mechanics, argued in his influential 1944 essay, "What Is Life," that indeterminacy could play no role. This essay had an enormous but unfortunate impact on the development of biology, especially on the work of Max Delbrück and other molecular biologists.

Glimcher writes:

[Schrödinger] argued that
fundamental indeterminacy would never arise in the living world because
if it were not so, if we were organisms so sensitive that a single atom, or even
a few atoms, could make a perceptible impression on our senses

Heavens,
what would life be like! To stress one point: an organism of that kind would
most certainly not be capable of developing the kind of orderly thought which,
after passing through a long sequence of earlier stages, ultimately results in
forming, among many other ideas, the idea of an atom. (Schrodinger 1944)

Our existing data, although ambiguous, clearly challenge Schrodinger’s conclusion.
The vertebrate nervous system is sensitive to the actions of single quantum
particles. At the lowest levels of perceptual threshold, the quantum dynamics of
photons, more than anything else, governs whether or not a human observer sees
a light. Synapses and neurotransmission also seem to violate
this assumption of Schrodinger’s, and these are the building blocks from
which neurocomputation is achieved. In the end, Schrodinger may be right, behavior
may be fundamentally determinate, but it would be premature to draw that
conclusion now. Behavioral scientists will have to continue to explore apparent
indeterminacy in behavior and will have to develop the methodological tools for
determining whether this apparent indeterminacy is fundamental.

(Indeterminacy in Brain and Behavior, pp.53-54)

Glimcher may be unaware of the deep philosophical reasons that led Schrödinger away from his early commitment to statistical views of physics (under the influence of his teacher Franz Exner and Ludwig Boltzmann). Schrödinger later became a hardened determinist along with Albert Einstein, Louis deBroglie, David Bohm, and others who challenged the indeterminacy of quantum physics to the ends of their lives.

After reviewing the research into stochastic behavior in neuron production of action potentials, Glimcher summarizes the likelihood that this indeterminacy might rise to the level of behavior.

The evidence that we have today suggests that membrane voltage can be influenced
by quantum level events, like the random movement of individual calcium
ions. So there is every reason to believe that membrane voltage can be viewed, at
least under some circumstances, as a formally indeterminate process of the type
that precludes Popperian falsifiability. How does this membrane voltage influence
action potential generation? Recall that cells receive a mixture of excitation and
inhibition from thousands of synapses and that the ratio of this mixture is variable.
Imagine that the correlations between the activity of the individual synapses
impinging on a given cell were variable. Under conditions in which the activity
of many synapses is correlated and the membrane voltage is driven either way
above or way below its threshold for action potential generation, the network of
neurons itself would maintain a largely determinate characteristic even though
the synapses themselves might appear stochastic. Alternatively, when the synaptic
activity is uncorrelated and the forces of excitation and inhibition are balanced,
small uncorrelated fluctuations in synaptic probabilities drive cells above or below
threshold. Under these conditions, indeterminacy in the synapses propagates to the
membrane voltage and thence to the pattern of action potential generation. Indeterminacy
in the pattern of action potential generation, although variable, would
reflect a fundamental indeterminacy in the nervous system.

At the level of behavior, apparent indeterminacy is reinforced by the environment
and has been observed. Animals can produce behavior that appears to
scientists to be indeterminate. How does this apparent indeterminacy arise? Given
what we know about the behavior of synapses and action potentials, two possibilities
present themselves. The fundamental indeterminacy observed at the cellular
level could be prevented from influencing higher-level phenomena in the nervous
system, rendering these higher-level phenomena determinate. These determinate
processes could then instantiate pseudorandom computations that emulate the underlying
cellular indeterminacy and yield apparently indeterminate behavior. Alternatively,
we can propose the hypothesis that indeterminacy observed at the cellular
level could propagate to behavior under some circumstances, yielding truly indeterminate
behavior under some conditions and more determinate behaviors under
others.

Among the first scientists to examine the pattern of cortical neuronal firing rates
with regard to indeterminacy were Tolhurst et al. (1981) and Dean (1981), who
were extending studies of neuronal variability pioneered by Barlow & Levick
(1969; see also Heggelund & Albus 1978). In two landmark papers, Tolhurst et al.
(1981) and Dean (1981) examined the firing patterns of neurons in the visual
cortices of anesthetized cats viewing visual displays that presented moving bars of
light.

What Tolhurst et al. (1981) and Dean (1981) found, therefore, was that at
the level of action potential generation, cortical neurons could be described as
essentially stochastic. This was a surprising result at the time, and it has been
widely confirmed (Rieke et al. 1997, Shadlen & Newsome 1998). What then is
the source of this apparent stochasticity, and would a more detailed biophysical
analysis of the spike generation mechanism reveal an underlying deterministic
process that would yield this apparent indeterminacy?

To examine one possible answer to that question, Mainen & Sejnowski (1995)
sought to determine whether the biophysical process that actually generates action
potentials in response to changes in membrane voltage was determinate...

They found that the spike-generating mechanism was fully
deterministic. A given pattern of membrane voltage gave rise to exactly the same
pattern of action potentials no matter how many times it was injected into the cell.

On the one hand, this was a reassuring result. At base, the pattern of action
potential generation was found to be governed by a determinate device. However,
on the other hand, it was puzzling. Spike rates are not determinate in this sense.
Tolhurst et al. and Dean’s work indicates that spike rates are distributed in a
Poisson-like fashion, and there clearly is nothing about the spike generator within
each cell that produces this pattern. The Mainen & Sejnowski (1995) data indicate
that the apparent randomness in spike patterns must be a function of apparent
randomness in the underlying membrane voltages. What then are the sources of
these Poisson-like fluctuations in membrane voltage?

We know that membrane voltages are governed, ultimately, by the pattern of
synaptic activations that a cell receives from the neurons that impinge upon it. Each
cortical neuron receives about 10,000 synapses from the tissue that surrounds it.
The fact that about half of these synapses are excitatory and half are inhibitory
is also important. It means that net excitation and inhibition are largely balanced
in an active neuron and small shifts in this balance cause the membrane voltage
to rise and fall, and thus cause action potentials to be generated. Together, these
observations make a clear suggestion. The source of the apparent stochasticity
in the membrane voltage either is a determinate pattern of synaptic activations
that carefully sculpts the membrane voltage to yield an apparently indeterminate
pattern of action potentials for reasons we do not yet understand or the process of
synaptic activation is itself apparently indeterminate.

A number of groups have investigated this latter possibility by studying the
activity of single synapses (see Auger & Marty 2000, Stevens 2003 for reviews of
this literature). The basic approach taken by these groups has been to activate a
neuron and then monitor the rate at which individual synaptic vesicles are released
into the synaptic cleft. Before these experiments were undertaken one could have
speculated that synapses were simple determinate mechanisms: When an action
potential invades the presynaptic region, it might be presumed that synaptic vesicles
of neurotransmitter were deterministically released into the synaptic cleft. Modern
studies of this process seem to contradict this view, however. Current evidence
indicates that when an action potential invades the presynaptic terminal, the chance
that a single synaptic vesicle will be released can be as low as 20%. Examinations
of the precise patterns of vesicular release suggest that the likelihood that a vesicle
of neurotransmitter will be released in response to a single action potential can
be described as a random Poisson-like process. Vesicular release seems to be an
apparently indeterminate process.

Careful study of other elements in the synapse seems to yield a set of similar, and
highly stochastic, results. Postsynaptic membranes, for example, seem to possess
only a tiny number of neurotransmitter receptors (cf. Takumi et al. 1999), and
during synaptic transmission as few as one or two of a given type of receptor
molecules may be activated (Nimchinski et al. 2004). Under these conditions, a
single open ion channel may allow a countable number of calcium or sodium ions
to enter the neuron, and there is evidence that the actions of a single receptor
and the few ions that it channels into the cell may influence the postsynaptic
membrane. Together, all of these data suggest that membrane voltage is the product
of interactions at the atomic level, many of which are governed by quantum physics
and thus are truly indeterminate events. Because of the tiny scale at which these
processes operate, interactions between action potentials and transmitter release
as well as interactions between transmitter molecules and postsynaptic receptors
may be, and indeed seem likely to be, fundamentally indeterminate.

In 1944, Schrodinger argued that the fundamental indeterminacy of the physical
universe would have no effect on living systems. He argued that were biological
systems to become so small that the actions of single atoms or molecules could
influence cells, the resulting organisms would surely perish from the evolutionary
landscape. Studies of the mammalian synapse, however, seem to indicate that
Schrodinger (1944) was simply wrong in this regard. Single synapses appear to
be indeterminate devices; not apparently indeterminate, but fundamentally indeterminate.
At base, physical indeterminacy seems to be a fundamental property
of the brain. But how sure can we be that this fundamental indeterminacy at the
level of the synapse has anything to do with indeterminacy at the level of a single
cortical neuron, at the level of a cortical network, at the level of behavior, or at the
level of a social theory of behavior?

The evidence that we have today suggests that membrane voltage can be influenced
by quantum level events, like the random movement of individual calcium
ions. So there is every reason to believe that membrane voltage can be viewed, at
least under some circumstances, as a formally indeterminate process of the type
that precludes Popperian falsifiability. How does this membrane voltage influence
action potential generation? Recall that cells receive a mixture of excitation and
inhibition from thousands of synapses and that the ratio of this mixture is variable.
Imagine that the correlations between the activity of the individual synapses
impinging on a given cell were variable. Under conditions in which the activity
of many synapses is correlated and the membrane voltage is driven either way
above or way below its threshold for action potential generation, the network of
neurons itself would maintain a largely determinate characteristic even though
the synapses themselves might appear stochastic. Alternatively, when the synaptic
activity is uncorrelated and the forces of excitation and inhibition are balanced,
small uncorrelated fluctuations in synaptic probabilities drive cells above or below
threshold. Under these conditions, indeterminacy in the synapses propagates to the
membrane voltage and thence to the pattern of action potential generation. Indeterminacy
in the pattern of action potential generation, although variable, would
reflect a fundamental indeterminacy in the nervous system.

At the level of behavior, apparent indeterminacy is reinforced by the environment
and has been observed. Animals can produce behavior that appears to
scientists to be indeterminate. How does this apparent indeterminacy arise? Given
what we know about the behavior of synapses and action potentials, two possibilities
present themselves. The fundamental indeterminacy observed at the cellular
level could be prevented from influencing higher-level phenomena in the nervous
system, rendering these higher-level phenomena determinate. These determinate
processes could then instantiate pseudorandom computations that emulate the underlying
cellular indeterminacy and yield apparently indeterminate behavior. Alternatively,
we can propose the hypothesis that indeterminacy observed at the cellular
level could propagate to behavior under some circumstances, yielding truly indeterminate
behavior under some conditions and more determinate behaviors under
others.